How the volume calculator works
Each shape has a standard formula. Here r is the radius (half the diameter) and h the height.
Cylinder: V = πr²h · A = 2πr(r + h)
Cone: V = πr²h ÷ 3 · A = πr(r + l), slant l = √(r² + h²)
Box: V = l × w × h · A = 2(lw + lh + wh)
Surface area includes the ends or base (the closed shape). Volume is in cubic units of whatever you measured with. A US gallon is 231 cubic inches and a liter is 1,000 cubic centimetres, so those conversions are shown for convenience. For a box, the radius field is used as the length.
Worked example
A cylindrical can with a radius of 3 in and a height of 5 in holds π × 9 × 5 = 141.37 cubic inches, about 0.61 US gallons, and has 150.8 square inches of surface area. A cone with radius 3 and height 4 has a slant height of 5, a volume of 37.70 and a surface area of 75.40. A sphere of radius 3 has a volume of 113.1.
Frequently asked questions
How do I find the volume of a cylinder?
Multiply π by the radius squared and by the height: V = πr²h.
Why is a cone one third of a cylinder?
A cone with the same base and height holds exactly one third of the cylinder's volume, a result known since Archimedes and Eudoxus.
How many gallons is a cubic foot?
About 7.48 US gallons (1,728 cubic inches ÷ 231).
Does surface area include the top and bottom?
Yes, the results are for closed shapes.
Updated October 2026. Results are estimates for education, not financial or medical advice. All math runs in your browser; nothing you type is sent anywhere.